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Chapter 4: Problem 42

From a point on level ground 30 yards from the base of a building, the angle of elevation is \(38.7^{\circ} .\) Approximate the height of the building to the nearest foot.

Short Answer

Expert verified
The height of the building is approximately 71 feet.

Step by step solution

01

Identify Given Information

The given information are as follows: angle of elevation \( \theta = 38.7^{\circ}\), distance from the building (adjacent side) = 30 yards.
02

Apply Tangent Ratio of a Right Triangle

Knowing that \( \tan(\theta) = \frac{opposite}{adjacent}\), we substitute the values into the equation, so \( \tan(38.7^{\circ}) = \frac{height}{30 yards}\) where height is the opposite side we are trying to find.
03

Solve for the Unknown

To solve for height, multiply both sides by 30 yards, therefore the equation becomes: height = 30 yards * \( \tan(38.7^{\circ})\).
04

Calculate Results

Using a calculator, compute the product which gives approximately 23.77 yards.
05

Convert Yards to Feet

We know that 1 yard is equivalent to 3 feet. Therefore, we have to multiply 23.77 yards by 3 to get the answer in feet. The solution, when rounded to the nearest foot, is approximately 71 feet.

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